The value of acceleration due to gravity depends on

Options

A. pressure
B. acceleration
C. gravitational force
D. none of these

Answer

To determine what the value of acceleration due to gravity depends on, we can analyze the formula for gravitational acceleration. The formula for gravitational acceleration \( g \) at a distance \( r \) from the center of the Earth is given by:

\[ g = \frac{G \cdot M}{r^2} \]

Where:
- \( g \) is the acceleration due to gravity,
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the Earth,
- \( r \) is the radius of the Earth (or the distance from the center of the Earth to the point where \( g \) is being measured).

### Step-by-Step Solution:

1. **Identify the Formula**: The formula for gravitational acceleration is \( g = \frac{G \cdot M}{r^2} \).

2. **Analyze the Components**:
- **Gravitational Constant \( G \)**: This is a constant value and does not change.
- **Mass of the Earth \( M \)**: This is a fixed value that does not change.
- **Radius \( r \)**: This is the distance from the center of the Earth to the point where we are measuring \( g \). For points on the surface of the Earth, this is equal to the radius of the Earth.

3. **Determine Dependencies**:
- From the formula, we can see that \( g \) depends on the mass of the Earth \( M \) and the radius \( r \).
- There are no terms in the formula that indicate dependence on pressure, acceleration, or gravitational force.

4. **Evaluate the Options**:
- **Option 1: Pressure** - Not present in the formula.
- **Option 2: Acceleration** - Not present in the formula.
- **Option 3: Gravitational Force** - While gravitational force is related to \( g \), the formula for \( g \) does not include gravitational force as a variable.
- **Option 4: None of these** - This is the correct choice since none of the other options affect the value of \( g \).

5. **Conclusion**: The value of acceleration due to gravity \( g \) depends solely on the mass of the Earth and the radius of the Earth. Therefore, the correct answer is **None of these**.